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A single-relaxation-time fluctuating lattice-Boltzmarm(LB)model for direct numerical simulation(DNS)of particle，s Brownian motion is established by adding a fluctuating component to the lattice-Boltzmann equations(LBEs)．The fluctuating term is proved to be the random stress tensor in fluctuating hydrodynamics by recovering Navier-Stokes equations from LBEs through a Chapman-Enskog expansion．A three-dimensional implementation of the model is also presented，along with simulations of a single spherical particle and 125 spherical particles at short times．Numerical results including the mean．square displacement．velocity autocorrelation function and self-diffusion coefficient of particles compare favorably with theoretical results and previous numerical resuits．